I'm assuming you mean Hydrazine. To initiate a decomposition of hydrazine, you need to provide an energy input called the activation energy. After that, the decomposition will release more energy, giving a net gain. Think of it like pushing a train up a small hill and over a steep cliff.
The action of the catalyst bed is to lower this activation energy so that the hydrazine "falls of the cliff" immediately. The upstream hydrazine would still require a large thermal input to decompose.
The thrusters and propulsion system are designed with thermal isolation to prevent heat soaking back into the rest of the propellant and doing just that.
The catalyst substrate is a material that can handle the temperature. There's some mechanics and thermal stresses as well, but these are manageable. Some catalyst is lost over time from these and other factors, but the rate is small enough that the beds are very long life. This is less true of the new ionic monopropellants like LMP-103S and AF-M315E. If you read the public literature, the reaction temperatures are higher, the combustion products more aggressive, and catalyst lifetime is still an issue in active work. Doesn't mean you can't use them, but it's still not as mature.
Titanium is a common material for tanks and lines. There are some specialty polymers for seals and other soft goods.
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